# MathSciDoc: An Archive for Mathematician ∫

#### Numerical Analysis and Scientific Computingmathscidoc:1702.25040

Bulletin of the Institute of Mathematics. Academia Sinica, 2, (4), 851-892, 2007.7
We present novel algorithms for compressible flows that\n\nare efficient for all Mach numbers. The approach is based on several\n\ningredients: semi-implicit schemes, the gauge decomposition\n\nof the velocity field and a second order formulation of the density\n\nequation (in the isentropic case) and of the energy equation (in\n\nthe full Navier-Stokes case). Additionally, we show that our approach\n\ncorresponds to a micro-macro decomposition of the model,\n\nwhere the macro field corresponds to the incompressible component\n\nsatisfying a perturbed low Mach number limit equation and\n\nthe micro field is the potential component of the velocity. Finally,\n\nwe also use the conservative variables in order to obtain a proper\n\nconservative formulation of the equations when the Mach number\n\nis order unity. We successively consider the isentropic case, the\n\nfull Navier-Stokes case, and the isentropic Navier-Stokes-Poisson\n\ncase. In this work, we only concentrate on the question of the\n\ntime discretization and show that the proposed method leads to\n\nAsymptotic Preserving schemes for compressible flows in the low\n\nMach number limit.
Mach number uniform method, Euler equations, Navier-Stokes equations, Asymptotic Preserving schemes, gauge schemes, compressible ﬂuids, Low-Mach number limit, macro-micro decomposition, semi-implicit scheme, Euler-Poisson system, Navier-Stokes-Poisson system.
```@inproceedings{pierre2007mach-number,
title={Mach-number uniform asymptotic-preserving Gauge schemes for compressible flows},
author={Pierre Degond, Shi Jin, and Jian-Guo Liu},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170209084030133546357},
booktitle={Bulletin of the Institute of Mathematics. Academia Sinica},
volume={2},
number={4},
pages={851-892},
year={2007},
}
```
Pierre Degond, Shi Jin, and Jian-Guo Liu. Mach-number uniform asymptotic-preserving Gauge schemes for compressible flows. 2007. Vol. 2. In Bulletin of the Institute of Mathematics. Academia Sinica. pp.851-892. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170209084030133546357.